The present disclosure relates generally to modal identification techniques for detecting dynamic properties of structures and more particularly to systems and methods for determining dynamic properties of structures with increased spatial resolution using one or more mobile sensors that collect vibration response data as they move through the structure.
Civil structures, such as bridges, buildings, and other structures, are extraordinarily important for society. Strategies to maintain or improve existing structural designs typically require numerical models of the structure to analyze behavior. The numerical models can be used to evaluate structure performance under specific conditions such as heavy loading, earthquake motion, wind loading, human activity, or other conditions. Developing accurate numerical models of existing structures is key to evaluate vulnerability, detecting damage, studying retrofit alternatives, predicting the useful life of structures, and performing other useful purposes. An accurate numerical model has the capability to reproduce the response of the real structure having parameters with a realistic physical meaning.
One way to validate an existing model is to compare the dynamic response of the numerical model with the actual response of the structure. Furthermore, the experimental response of the structure can be used to update or improve those numerical models. System identification and modal analysis techniques are used to determine modal parameters of a structure, including natural frequencies, mode shapes, and modal damping ratios. Different types of dynamic tests or excitations can be applied to the structure to characterize its behavior, such as free vibration, sinusoidal excitation, impulse excitation, and resonance tests. The use of ambient vibration, generally caused by traffic, wind, and microtremors, under normal operating conditions for the structure, can be a preferred approach for civil structures such as bridges.
In a traditional modal identification system, a finite number of sensors are placed at strategic points. For instance, FIG. 1 illustrates an exemplary modal identification system 50 that includes a plurality of sensors 52, 54, 56, and 58 placed at key locations on structure 60. The coordinates of the modes shapes of structure 60 are calculated only at the location of sensors 52, 54, 56, and 58. As shown in FIG. 2, this creates a low spatial resolution mode shape. As illustrated, curve 70 illustrates the expected mode shape of the structure 60, while curve 72 represents the identified mode shape obtained with the data from the stationary sensors.
One approach to addressing low spatial resolution is to install additional sensors. However, the cost of instrumentation and installation of dense sensor networks can be prohibitive. Smart wireless sensors have been proposed for large instrumentation systems. The relative lower cost of the sensors and easier installation of the wireless sensors makes them more suitable for dense sensor networks. However, there are still fundamental challenges faced by this technology such as battery life and overload of the communication network.
Another approach to addressing low spatial resolution is mode shape expansion. Mode shape expansion is used to calculate the complete mode shape based on the information of discrete points. Exemplary mode shape expansion techniques include i) spatial interpolation techniques, which use a finite element model geometry to expand the mode shape; ii) properties interpolation techniques, which use the finite element model properties for the expansion; and iii) error minimization techniques, which intend to reduce the error between the expanded and the analytical mode shapes using projection methods. Mode shape expansion can introduce errors due to, for instance, discrepancies in the location of the sensors in the actual structure and numerical models, measurement errors, modeling errors, and other factors.
Another existing modal identification technique involves the use of Laser Doppler Vibrometers (LDVs) in a continuously scanning mode. A laser beam from the LDV is focused to a surface of interest and the velocity of the addressed point is measured using the Doppler shift between the incident and the reflected beam. Vibration measurements along a line can be made by continuously passing the laser beam over the surface of a vibrating structure. The single signal collected from the LDV at uniform or sinusoidal speed can be used for the identification of a polynomial that describes the operational mode shape of a structure. A continuous scan LDV (CSLDV) can be used to derive curvature equations of a structure and to calculate the stress and strain distributions for the structure. For instance, CSLDV can be used in conjunction with random excitation of a structure to identify operational deflection shapes for maintaining a polynomial shape assumption.
The use of LDV or CSLDV technology in the identification of mode shapes for structures, and in particular for civil infrastructure such as bridges and buildings, poses several challenges. For instance, the usable distance of the lasers is typically too small for most civil applications and line of sight is often needed. In addition, LDV and CSLDV systems are relatively expensive. Moreover, LDV and CSLDV measurements can be distorted due to the exposure of a structure to environmental factors, leading to reduced reliability.
Thus, there is a need for a system and method for modal identification that can be implemented using a reduced number of sensors and that can provide for increased spatial resolution of the mode shape that overcomes the above-mentioned disadvantages.